On the use of state-observers in compartmental systems control

In this paper, we analyse the performance of state-observers in the control of compartmental systems under the presence of uncertainties in the system initial state. We combine a state feedback law with positivity constraints and a state observer and prove that, as expected, the mass control objective is still attained. Moreover we show that, for a class of three-compartmental systems of interest, the resulting mass control law also allows reaching a desired steady state. Our results are illustrated by several simulations for the control of the administration of a neuromuscular relaxant to patients undergoing surgery, which show the relevance of incorporating an observer for convergence acceleration even in case the original system is asymptotically stable.